Calculus 2, Lecture 10A, Intro to Velocity Vectors, Numerical Integration on Mathematica

Calculus 2, Lecture 10A.

(0:00) Gateway information.
(4:11) Summary of lecture.
(5:06) Representing vectors in terms of standard unit vectors ("i hat" and "j hat").
(9:04) Plot a parametric (Lissajous) curve on Mathematica along with the position vector.
(10:05) The formula for the velocity vector and getting it into Mathematica (based at the location of the object as it moves). Interpret its length and direction.
(14:26) Use NIntegrate on Mathematica to help plot the speed (red) and distance traveled (blue) functions.
(16:15) Programming left- and right-hand sum approximations, as well as the trapezoid rule, into Mathematica to estimate the distance traveled for an interval on which speed(t) is decreasing.
(27:29) Quantifying the errors as exact value - estimate.
(28:58) Introduction to the midpoint rule and its error.